Chapter 4.5, Problem 21PPS

To determine

To prove:

The two seats stay of the same length

Explanation of Solution

Given information:

  

Proof:

From the given figure:

  

The two seats are $AC$ and $AD$

Know that:

  $\begin{array}{l}m\angle ACB=44°\\ m\angle ADB=44°\\ m\angle CBA=68°\\ m\angle DBA=68°\end{array}$

So, substitution for the given angles is:

  $\begin{array}{l}m\angle ACB=m\angle ADB=44°\\ m\angle CBA=m\angle DBA=68°\end{array}$

According to the definition congruence:

  $\angle ACB\cong \angle ADB,\angle CBA=\angle DBA$

According to the reflexive property:

  $\overline{AB}\cong \overline{AB}$

According to angle-angle (AAS) congruence postulate:

  $\Delta ADB\cong \Delta ACB$

Know that: the corresponding parts of congruent triangles are congruent;

  $\overline{AC}\cong \overline{AD}$

Hence proved